All models in Law and Economics use punishment functions (PF) that incorporates a trade-off between probability of detection, p, and punishment, F . Suppose society wishes to minimize the total costs of enforcement and damages from crime, T (p, F ). For a given p, an optimal punishment function (OPF) determines an F that minimizes T (p, F ). A popular and tractable PF is the hyperbolic punishme...

In this paper, first the space of hyperbolic tangent functions is introduced and then the universal approximator property of this space is proved. In fact, by using this space, any nonlinear continuous function can be uniformly approximated with any degree of accuracy. Also, as an application, this space of functions is utilized to design feedback control for a nonlinear dynamical system.

in this paper, a new t-s fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. fuzzy controller is designed based on the parallel distributed compensation (pdc), and with a new lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...

Subadditive time discounting means that discounting over a delay is greater when the delay is divided into subintervals than when it is left undivided. This may produce the most important result usually attributed to hyperbolic discounting: declining impatience, or the inverse relationship between the discount rate and the magnitude of the delay. Three choice experiments were conducted to test ...

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...

We will investigate the superstability of the hyperbolic trigonometric functional equation from the following functional equations: fx y ± gx − y λfxgy andfx y ± gx − y λgxfy, which can be considered the mixed functional equations of the sine function and cosine function, the hyperbolic sine function and hyperbolic cosine function, and the exponential functions, respectively.

Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F (x) = ? lo...

Hyperbolic fibrations of PG(3, q) were introduced by Baker, Dover, Ebert and Wantz in [1]. Since then, many examples were found, all of which are regular and agree on a line. It is known, via algebraic methods, that a regular hyperbolic fibration of PG(3, q) that agrees on a line gives rise to a flock of a quadratic cone in PG(3, q), and conversely. In this paper this correspondence will be exp...

1. Error calculus 2 1.1. Ulp calculus 2 1.2. Relative error analysis 4 1.3. Generic error of addition/subtraction 4 1.4. Generic error of multiplication 5 1.5. Generic error of inverse 5 1.6. Generic error of division 6 1.7. Generic error of square root 7 1.8. Generic error of the exponential 7 1.9. Generic error of the logarithm 8 1.10. Ulp calculus vs relative error 9 2. Low level functions 9...

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative e...